IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v17y2017i9p1387-1401.html
   My bibliography  Save this article

How much is the gap?—Efficient jump risk-adjusted valuation of leveraged certificates

Author

Listed:
  • Ally Quan Zhang
  • Matthias Thul

Abstract

This paper develops a novel and highly efficient numerical algorithm for the gap risk-adjusted valuation of leveraged certificates. The existing literature relies on Monte Carlo simulations, which are not fast enough to be used in a market-making environment. This is because issuers need to compute thousands of price updates per second. By valuing leveraged certificates as multi-window barrier options, we explicitly model random jumps that occur at known times, such as between the exchange closing and re-opening. Our algorithm combines the one-day transition probability with Simpson’s numerical integration rule. This yields a backward induction scheme which requires a significantly coarser spatial and time grid than finite-difference methods. We confirm its robustness and accuracy through Monte Carlo simulations.

Suggested Citation

  • Ally Quan Zhang & Matthias Thul, 2017. "How much is the gap?—Efficient jump risk-adjusted valuation of leveraged certificates," Quantitative Finance, Taylor & Francis Journals, vol. 17(9), pages 1387-1401, September.
  • Handle: RePEc:taf:quantf:v:17:y:2017:i:9:p:1387-1401
    DOI: 10.1080/14697688.2016.1276299
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2016.1276299
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/14697688.2016.1276299?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Boes, Mark-Jan & Drost, Feike C. & Werker, Bas J. M., 2007. "The Impact of Overnight Periods on Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(2), pages 517-533, June.
    2. Baller, Stefanie & Entrop, Oliver & McKenzie, Michael & Wilkens, Marco, 2016. "Market makers’ optimal price-setting policy for exchange-traded certificates," Journal of Banking & Finance, Elsevier, vol. 71(C), pages 206-226.
    3. Entrop, Oliver & Scholz, Hendrik & Wilkens, Marco, 2009. "The price-setting behavior of banks: An analysis of open-end leverage certificates on the German market," Journal of Banking & Finance, Elsevier, vol. 33(5), pages 874-882, May.
    4. Wilkens, Sascha & Stoimenov, Pavel A., 2007. "The pricing of leverage products: An empirical investigation of the German market for `long' and `short' stock index certificates," Journal of Banking & Finance, Elsevier, vol. 31(3), pages 735-750, March.
    5. Peter Buchen, 2004. "The pricing of dual-expiry exotics," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 101-108.
    6. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    7. Ingersoll, Jonathan E, Jr, 2000. "Digital Contracts: Simple Tools for Pricing Complex Derivatives," The Journal of Business, University of Chicago Press, vol. 73(1), pages 67-88, January.
    8. Rossetto, Silvia & Bommel, Jos van, 2009. "Endless leverage certificates," Journal of Banking & Finance, Elsevier, vol. 33(8), pages 1543-1553, August.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Baller, Stefanie & Entrop, Oliver & Schober, Alexander & Wilkens, Marco, 2017. "What drives performance in the speculative market of short-term exchange-traded retail products?," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe B-26-17, University of Passau, Faculty of Business and Economics.
    2. Entrop, Oliver & Fischer, Georg, 2019. "Hedging costs and joint determinants of premiums and spreads in structured financial products," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe B-34-19, University of Passau, Faculty of Business and Economics.
    3. Entrop, Oliver & Scholz, Hendrik & Wilkens, Marco, 2009. "The price-setting behavior of banks: An analysis of open-end leverage certificates on the German market," Journal of Banking & Finance, Elsevier, vol. 33(5), pages 874-882, May.
    4. Schertler, Andrea, 2016. "Pricing effects when competitors arrive: The case of discount certificates in Germany," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 84-99.
    5. Baller, Stefanie & Entrop, Oliver & McKenzie, Michael & Wilkens, Marco, 2016. "Market makers’ optimal price-setting policy for exchange-traded certificates," Journal of Banking & Finance, Elsevier, vol. 71(C), pages 206-226.
    6. Oliver Entrop & Georg Fischer, 2020. "Hedging costs and joint determinants of premiums and spreads in structured financial products," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(7), pages 1049-1071, July.
    7. Schertler, Andrea, 2021. "Listing of classical options and the pricing of discount certificates," Journal of Banking & Finance, Elsevier, vol. 123(C).
    8. Baule, Rainer, 2011. "The order flow of discount certificates and issuer pricing behavior," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 3120-3133, November.
    9. Baller, Stefanie, 2017. "Risk taking in the market of speculative exchange-traded retail products: Do socio-economic factors matter?," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe B-27-17, University of Passau, Faculty of Business and Economics.
    10. H. Fink & S. Geissel & J. Sass & F. T. Seifried, 2019. "Implied risk aversion: an alternative rating system for retail structured products," Review of Derivatives Research, Springer, vol. 22(3), pages 357-387, October.
    11. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    12. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    13. Kevin Fergusson & Eckhard Platen, 2006. "On the Distributional Characterization of Daily Log-Returns of a World Stock Index," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 19-38.
    14. Robert Elliott & Tak Siu, 2015. "Asset Pricing Using Trading Volumes in a Hidden Regime-Switching Environment," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(2), pages 133-149, May.
    15. Lars Stentoft, 2008. "Option Pricing using Realized Volatility," CREATES Research Papers 2008-13, Department of Economics and Business Economics, Aarhus University.
    16. repec:uts:finphd:40 is not listed on IDEAS
    17. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    18. Hyong-Chol O & Mun-Chol KiM, 2013. "The Pricing of Multiple-Expiry Exotics," Papers 1302.3319, arXiv.org, revised Aug 2013.
    19. René Garcia & Richard Luger & Éric Renault, 2005. "Viewpoint: Option prices, preferences, and state variables," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(1), pages 1-27, February.
    20. Mr. Noureddine Krichene, 2006. "Recent Dynamics of Crude Oil Prices," IMF Working Papers 2006/299, International Monetary Fund.
    21. Bucsa, G. & Jovanovic, F. & Schinckus, C., 2011. "A unified model for price return distributions used in econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3435-3443.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:quantf:v:17:y:2017:i:9:p:1387-1401. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.